Observer-based stabilization of switched discrete-time linear systems with parameter uncertainties: New scenarios of LMI conditions

This chapter deals with the problem of observer-based controller design via linear matrix inequalities for a class of switched discrete-time linear systems. The main contribution consists of providing different scenarios of the use of Finsler’s lemma to reduce the conservatism of some of the existing results in the literature. Thanks to these scenarios, and the use of some other new mathematical tools, one of the objectives of this chapter is to open new research directions for other control design problems. The effectiveness and superiority of the proposed design methodologies are shown through numerical examples.